Problem: Simplify the following expression: $q = \dfrac{9}{81p - 18}$ You can assume $p \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $9 = (3\cdot3)$ The denominator can be factored: $81p - 18 = (3\cdot3\cdot3\cdot3 \cdot p) - (2\cdot3\cdot3)$ The greatest common factor of all the terms is $9$ Factoring out $9$ gives us: $q = \dfrac{(9)(1)}{(9)(9p - 2)}$ Dividing both the numerator and denominator by $9$ gives: $q = \dfrac{1}{9p - 2}$